My Research

I have worked on several directions for research.

Orbifolds:

• My Thesis (Riemannian Orbifolds with Non-Negative Curvature)
• Orbifold Biquotients of SU(3) (arXiv link) Published: Diff. Geom. Appl. 42, (2015) 54-76
• On Poincaré Duality for Orbifolds (arXiv link) Published: Topology Appl. 219, (2017) 9-16
• On Geometry and Topology of 4-Orbifolds (arXiv link) Pre-print

Manifolds with Density:

• On the geometry of Riemannian manifolds with density (with W. Wylie) (arXiv link) Pre-print
• The weighted connection and sectional curvature for manifolds with density (with L. Kennard and W. Wylie) (arXiv link) Published: J Geom Anal. 29, (2019) 957–1001
• Holonomy of Manifolds with Density (arXiv link) Pre-print

Other Geometry:

• Ricci Flow on Torus Bundles (arXiv link) Pre-print

Other topics:

• On Levine's notorious hat puzzle (with J. Buhler, C. Freiling, R. Graham, J. Kariv, J.R. Roche, M. TIefenbruck and C. Van Alten) (arXiv link) Integers 21A, (2021) A8.1-52 PDF on Journal site
• Connectedness of two-sided group digraphs and graphs (with P. Chikwanda, C. Kriloff, Y.T. Lee, T. Sandow and G. Smith) (arXiv link) Involve 11, (2018) 679-699
  Note: This paper was a student research project at Idaho State University under the direction of Cathy Kriloff which I joined as a second faculty supervisor part-way through.